# Thread: Solving Equations using Logs

1. ## Solving Equations using Logs

I have been set a question f = (uv)/(u+v) I have to solve for v using logarithms. I had done several examples and am confident but not one in this format. Can any one help with a stage by stage how to do? I can do a lot more that seem more complicated but I miss small things sometimes that make the difference. Thanks loads and hope to hear from someone who can put my mind at rest.

2. ## Re: Solving Equations using Logs

So you need to find v in terms of u and f, and you have to use logarithms? That's a very strange problem, is this a homework problem or text book problem where you can state the actual problem?

YOu can take natural log of both sides:

$ln(f)=ln\right(\frac{uv}{u+v}\left$

and on the right side use the rules of logarithms to expand, and then try to isolate v.

$ln(xy)=ln(x)+ln(y)$

$\ln (\right\frac{x}{y}\left)=ln(x)-ln(y)$

$e^{ln(x)}=x$.

3. ## Re: Solving Equations using Logs

Adkin's jr's "laws of logarithms" are correct but unfortunately there is no "law of logarithms that will allow you to simplify log(u+ v).

There is simply no reason to use logarithms to solve this equation- it isn't necessary and it doesn't work!

Instead, if f= uv/(u+ v) then f(u+ v)= fu+ fv= uv so that uv- fv= (u- f)v= fu and then v= fu/(u- f).

4. ## Re: Solving Equations using Logs

Thank you very much. If I am completely honest this equation was not 100% clear it had to be solved using logs. Although my assignment had nothing but log and natural logs which left me confused.

5. ## Re: Solving Equations using Logs

Hi again..thanks for your help I have

(3.4)^2x+3=8.5 for x

I got as far as

(3.4)2x+3=8.5
(2x+3)log(3.4) = log(8.5)
(2x+3)x0.531 = 0.929
(2x+3)x1.062 = 0.929

then got stuck. The nearest I have got to an answer of 8.5 was 0.87. Out by an order of magnitude!!!

6. ## Re: Solving Equations using Logs

Hi again..thanks for your help I have

(3.4)^2x+3=8.5 for x

I got as far as

(3.4)2x+3=8.5
(2x+3)log(3.4) = log(8.5)
(2x+3)x0.531 = 0.929
(2x+3)x1.062 = 0.929

then got stuck. The nearest I have got to an answer of 8.5 was 0.87. Out by an order of magnitude!!!